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Add MAA MPP Model to docs/theory
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jakep72 committed Feb 22, 2024
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2 changes: 1 addition & 1 deletion docs/Theory/EF_MPP_Model.md
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Expand Up @@ -38,7 +38,7 @@ and $eps$ is:
eps = 2\sqrt{\frac{\phi}{\pi}}
\]

The [Add_MPP_EF_Layer](https://jakep72.github.io/acoustipy/AcousticTMM/#src.acoustipy.TMM.AcousticTMM.Add_MPP_EF_Layer) method then converts The modified dynamic mass density and bulk modulus to the characteristic impedence $(Z_{c})$ and wavenumber $(k_{c})$ for use in the layer transfer matrix.
The [Add_MPP_EF_Layer](https://jakep72.github.io/acoustipy/AcousticTMM/#src.acoustipy.TMM.AcousticTMM.Add_MPP_EF_Layer) method then converts the modified dynamic mass density and bulk modulus to the characteristic impedence $(Z_{c})$ and wavenumber $(k_{c})$ for use in the layer transfer matrix.

\[
Z_{c} = \sqrt{\tilde{\rho}\widetilde{K}}
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77 changes: 77 additions & 0 deletions docs/Theory/MAA_MPP_Model.md
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# MAA MPP Model

The Maa microperforate model determines the characteristic impedence $(Z_{c})$ of the layer based on the perforate diameter $(d)$, center-to-center distance $(b)$, and thickness $(t)$.

Unlike other material models, the Maa MPP model does not calculate a characteristic wavenumber $(k_{c})$. Instead, a separate transfer matrix is used.

# Determination of Characteristic Impedence

\[
Z_{c} = r+j\omega m
\]

where $r$ is:

\[
r = \frac{32\eta t}{\phi d^2} r_{1}
\]

\[
r_{1} = \sqrt{1+\frac{x^2}{32}}+\frac{\sqrt{2}}{32} x \frac{d}{t}
\]

$m$ is:

\[
m = \frac{\rho_{0}t}{\phi} m_{1}
\]

\[
m_{1} = 1+\frac{1}{\sqrt{1+\frac{x^2}{2}}}+\frac{0.85d}{t}
\]

and

\[
x = \frac{d}{2}\sqrt{\frac{\omega\rho_{0}}{\eta}}
\]

\[
\phi = \frac{\pi}{4}\Bigg(\frac{d}{b}\Bigg)^2
\]

The characteristic impedence $(Z_{c})$ is then used directly in the layer transfer matrix via the [Add_MAA_MPP_Layer](https://jakep72.github.io/acoustipy/AcousticTMM/#src.acoustipy.TMM.AcousticTMM.Add_MAA_MPP_Layer) method.


## Model Parameters:

##### Using the following nomenclature --- Symbol = [Units] (name)

\[
d = \Bigg[m\Bigg]\tag{perforate diameter}
\]

\[
b = \Bigg[m\Bigg]\tag{center-to-center distance}
\]

\[
t = \Bigg[m\Bigg]\tag{layer thickness}
\]


## Defining Other Symbols:

##### Using the following nomenclature --- Symbol = [Units] (name)

\[
\rho_{0} = \Bigg[\frac{kg}{m^3}\Bigg]\tag{air density}
\]

\[
\eta = \Bigg[Pa*s\Bigg]\tag{viscosity of air}
\]

\[
\omega = \Bigg[\frac{radians}{s}\Bigg]\tag{angular frequency}
\]
14 changes: 0 additions & 14 deletions docs/Theory/TMM_Theory_General.md
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### ***The Theory section is under active development***
- Porous Material Models
- [x] [DB Model](https://jakep72.github.io/acoustipy/Theory/DB_Model/)
- [x] [DBM Model](https://jakep72.github.io/acoustipy/Theory/DBM_Model/)
- [x] [JCA Model](https://jakep72.github.io/acoustipy/Theory/JCA_Model/)
- [x] [JCAL Model](https://jakep72.github.io/acoustipy/Theory/JCAL_Model/)
- [x] [JCAPL Model](https://jakep72.github.io/acoustipy/Theory/JCAPL_Model/)
- [x] [Horoshenkov Model](https://jakep72.github.io/acoustipy/Theory/Horoshenkov_Model/)
- [x] [Biot-Limp Model](https://jakep72.github.io/acoustipy/Theory/Biot_Limp_Model/)
- [x] [Biot-Rigid Model](https://jakep72.github.io/acoustipy/Theory/Biot_Rigid_Model/)
- [x] [Resistive Screen Model](https://jakep72.github.io/acoustipy/Theory/Resistive_Screen_Model/)
- Microperforate Models
- [ ] [MAA Model](https://jakep72.github.io/acoustipy/Theory/MAA_MPP_Model/)
- [ ] [EF Model](https://jakep72.github.io/acoustipy/Theory/EF_MPP_Model/)
### All models and methods described in the Theory section align with the code implementation.

### For each material model, an array of values corresponding to the complex characteristic impedance $(Z_{c})$ and wavenumber $(k_{c})$ are generated and used to calculate that layer's transfer matrix.
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2 changes: 1 addition & 1 deletion mkdocs.yml
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Expand Up @@ -54,7 +54,7 @@ nav:
- Inverse Method: Examples/Inverse.md
- Indirect Method: Examples/Indirect.md
- Hybrid Method: Examples/Hybrid.md
- Theory -- under active development:
- Theory:
- AcousticTMM:
- Overview: Theory/TMM_Theory_General.md
- Porous Material Models:
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